Derivation of Lorentz Transformation via Lorentz Invariant

摘要

We derive the Lorentz transformation matrix via the invariance of spacetime interval. The derivation is greatly simplified by using hyperbolic functions. The Lorentz scalar and the 4-vector are explained via the concept of relativistic covariance and the results are applied to relativistic mechanics. This paper helps to better understand the mathematical structure of special relativity, and may be useful for engineers working with relativistic applications such as satellite navigation and precision chronometry.